This is a renewal application for methodological research in statistical issues related to community-based or observational studies in cancer and environmental epidemiology. A general class of semiparametric transformation models is proposed for multivariate survival data, providing a unified likelihood framework that allows the regression coefficients to have population-level interpretations and the dependence parameters to be conveniently modeled. Specifically, the PI plans to develop: (1) Semiparametric normal transformation Cox models for multivariate survival data: Flexible modeling of pairwise dependence will be developed and a new class of marginalized frailty models will be proposed. Semiparametric maximum likelihood estimation approach will be investigated. We will further consider generalized semiparametric normal transformation survival models, encompassing the proportional hazards and the proportional odds models as special cases;(2) Accelerated semiparametric normal transformation models for multivariate survival data: We will propose a new semiparametric normal transformation AFT model by exploring the mean structure of the failure times. We will develop consistent and numerically stable inference procedures, and investigate their large sample results;(3) Multivariate survival models with non negligible cure fractions: Two new classes of models, semiparametric frailty cure models and semiparametric normal transformation cure models will be proposed. Theoretical properties for both classes of models will be explored and feasible inference procedures will be investigated. The extension to a spatial setting will be considered;(4) Clustered recurrent event models with covariate measurement errors and delayed entry: two new classes of recurrent event models will be proposed to account for within-cluster correlations, mismeasured covariates and delayed entry. Properties of the models will be investigated and various inference procedures will be proposed. Empirical data analyses will playa central role in all the specific aims. Available data stem from several cancer and environmental health projects that the PI has been involved in, namely, the NCI-funded Cancer Care Outcomes Research and Surveillance Consortium (CanCORS), the Young Worker Smoking Cessation Intervention study (a randomized community-based cancer prevention trial), the NIH SEER cancer incidence database, the West Kenya Malaria Study and the Home Allergen Study. Although motivated by applied problems, the proposed research offers useful contributions to general statistical theory and methodology in survival analysis, multivariate statistical analysis, cure models and measurement error modeling.